Magnetic resonance imaging (MRI) is an imaging technique used to form images of the anatomy and functions of the body. This section is taken from the author’s project thesis, written during the fall semester of 2019, with minor adjustments, and it is based on the book MRI in Practice [17] unless other is stated.
MRI is an imaging technique used to form images of the anatomy and functions of the body. The technique is based on the spin and magnetic moment of nuclei.
An MR active nucleus has an odd mass number and therefore a net spin. Nuclei with a net charge and spin will have a magnetic moment, the same way as a current moving through a coil induces a magnetic field. In this case, the nuclei then act as a small magnet. In human applications hydrogen (1H) is the most used nuclei because of its relatively large magnetic moment, and the fact that a large amount of the body consists of water which means that it is a lot of hydrogen available. The spins are randomly oriented, but when an external magnetic field is applied, the nuclei tend to align their axis of rotation to the magnetic field.
They can align parallel or anti-parallel to the field, and there is a slight preference for parallel because this corresponds to a lower energy state. This leads to a net magnetization in the direction of the magnetic field. The spins will precess around the magnetic field, B0, with a frequency, called the Larmor frequency,w0.
w0 =γB0, (2.1)
whereγ is the gyromagnetic ratio which expresses the relationship between the magnetic moment and the angular momentum. This is a constant specific to the nuclei type.
A radio frequency pulse can be applied at the Larmor frequency to excite the spins. By exciting the spins, the net magnetization vector can be moved away from alignment withB0. The flip angle is referred to as the angle the net magnetization vector is moved out of alignment, and this angle is often90◦. That will say that the net magnetization is moved from the longitudinal plane to the transverse plane.
The nuclei will then precess in the transverse plane and produce magnetic field fluctuations inside a receiver coil. This induces an electrical voltage, and this is
3
the MR signal. The net magnetization vector will try to realign with theB0 field, and in this process, the nuclei transfer energy to the surroundings. A decrease in the magnetization in the transverse plane and recovery of the magnetization in the longitudinal plane will then occur. This is called T1 relaxation. It is an exponential process, and the time it takes for 63% of the longitudinal magnetization to recover is called T1.
The spins in the transverse plane will start in phase after the excitation pulse and then dephase. This dephasing is due to spin-spin interactions, T2, and inho-mogeneities in the magnetic field, T2’. The T2’ dephasing is a systematic effect that can be reversed, while T2 is a random effect and varies with the nuclei type.
The total dephasing is referred to as T2* decay, and the relationship between T2, T2’ and T2* is given by the following equation.
1
T2∗ = 1 T2+ 1
T20 (2.2)
In MR sequences the repetition time, TR, is the time from the application of the excitation pulse to the application of the next excitation pulse. This time determines the amount of T1 relaxation that is allowed to occur before the signal readout. The echo time, TE, is the time from the application of the excitation pulse to the peak of the signal that is induced in the receiver coil. This determines how much T2 relaxation that is allowed to happen before the readout.
A spin-echo sequence is one of the most used pulse sequences in MRI. In this sequence, a 90◦ excitation pulse is applied to flip the net magnetization to the transverse plane. A free induction decay signal will occur, and after a time TE/2 a 180◦ pulse is applied to rephase the spins and we get a spin echo signal at TE.
Figure 2.1 shows a vector representation of the dephasing and rephasing of the spins.
To form an image it is important to determine the spatial location of the signal.
This is done with the use of magnetic field gradients. The Larmor frequency is dependent on the magnetic field strength, and a nucleus experiencing a high mag-netic field strength will have a lager Larmor frequency than a nucleus experiencing a lower field strength. To select a slice in the z-direction, often the direction from feet to head of a patient, a gradient is applied in theB0 direction. The Larmor fre-quency of the spins will now vary along the z-direction. The excitation pulse with a band of frequencies equal to the Larmor frequencies of the spins in the wanted slice is applied, and only spins in this slice will get excited. The slice thickness is dependent on the bandwidth of the pulse and the steepness of the gradient. In a spin-echo sequence, the slice selection gradient is on during the90◦ and180◦ radio frequency pulse. The two remaining directions are called the frequency encoding direction and the phase encoding direction. A gradient in the frequency encoding direction is switched on during the readout of the signal. Signals from different locations along this gradient will have different frequencies. In the phase encoding direction, a gradient is applied after the excitation pulse. This gradient is only on for a given amount of time and induces a phase shift between spins along the phase encoding gradient. The resulting pulse sequence with all the gradients is shown in figure 2.2.
In phase Dephasing After 180o pulse Rephasing
Figure 2.1: Vector representation of the spin dephasing and rephasing in a spin-echo sequence. The blue arrow represents the spins that rotate at the Larmor frequency, the green arrow represents the spins that rotates a bit faster and the red arrow represents the spins that rotate a bit slower.
TE/2 TR
TE
90o 180o 90o
RF
GSS
GPE
GFE
Signal FID Echo
Figure 2.2: Spin echo pulse sequence and spatial encoding gradients. RF is the radio frequency pulses,GSS is the slice selecting gradient,GP E is the phase encoding gradient and GF E is the frequency encoding gradient.
The recorded signal is mapped to a spatial frequency domain, the so-called k-space. The horizontal lines correspond to the frequency encoding while the vertical lines correspond to the phase encoding. A 2D Fourier Transform is applied to reconstruct the image from k-space.
By applying different pulse sequences, different contrasts can be obtained in the images. It is possible to have sequences that highlight the anatomy but also sequences that highlight functional properties like diffusion.
2.1.1 T2 weighted images
In T2 weighted images, water/fluid will appear bright, fat will appear intermediate-bright, while air and muscle will appear dark. This can be seen in the T2 weighted image in figure 2.3. The image contrast is a result of the fact that different tissues have different T2. Fat molecules can easily absorb energy into its lattice from the hydrogen nuclei due to low inherent energy. From this, it follows that the lon-gitudinal magnetization is able to recover quickly in fat, and fat has a short T1.
Water, on the other hand, has high inherent energy and does not absorb energy into its lattice easily. Because of this, it takes water a longer time to recover the longitudinal magnetization and it has a long T1. The fat molecules are packed closely together, and spin-spin interactions are likely to occur. The spins in fat will dephase quickly, which leads to a short T2. The spin-spin interactions are less likely to occur in water because there is more space between the molecules, and water has a long T2.
To get a T2 weighted image the difference in T2 for water and fat needs to be enhanced, and the difference in T1 needs to be diminished. This can be controlled by adjusting TE and TR. The TE must be long enough so that both fat and water have time to decay. Since water has the longest T2, it will be most signal left from water. The TR must be so long that both water and fat get time to fully recover their longitudinal magnetization, and therefore the difference in T1 will not create contrast in the image.
Figure 2.3: A T2 weighted image of a patient with rectal cancer. The red arrow points at the tumor.
2.1.2 Diffusion weighted images
Diffusion is referred to as the random Brownian motion of molecules driven by thermal energy [18]. In a perfectly homogeneous medium, the probability for motion will be the same in all directions, and there will be free diffusion. This is not the case in a complex environment like the human body. In the body, there are intracellular and extracellular compartments. In the extracellular regions, the water molecules will experience a relatively free diffusion while there will be a more restricted diffusion in the intracellular regions. Different tissues have different proportions of intra- and extracellular compartments and characteristic cellular architecture. This means that the diffusion properties vary with the tissue. In tumors, there is a higher cell density than in healthy tissue, and this results in a more restricted diffusion.
In a diffusion weighted image (DWI) the contrast is determined by the diffusion of water molecules [19]. The presence of a magnetic field gradient will cause a phase shift in the spins, and the cumulative phase shift,φ, for a single static spin is given by
φ(t) =γB0t+γ Z t
0
G(t0)·x(t0)dt0. (2.3) In equation (2.3) the first term is due to the static B0-field and the second term is due to a magnetic field gradient. G is the strength of the gradient, x is the spatial location of the spin and t is the duration of the gradient.
A normal pulse sequence in DW imaging consists of a T2-weighted spin-echo sequence and two equal gradient pulses applied before and after the180◦refocusing pulse. This is called a Stejskal-Tanner sequence [20], and it is shown in figure 2.4.
The phase shift due to the applied gradient will for an individual spin be proportional to the displacement of the spin along the direction of the gradient [19]. At the echo time, TE, the total phase shift for a particular spin is equal to
90o 180o
Signal FID Echo
Gradients RF
Figure 2.4: Stejskal-Tanner sequence consisting of a spin echo pulse sequence together with the diffusion gradients used in diffusion weighted imaging.
φ(T E) =γ Z t1+δ
t1
G(t0)·x(t0)dt0−γ
Z t1+∆+δ
t1+∆
G(t0)·x(t0)dt0. (2.4) Here δ is the time the gradient is applied for and ∆ is the time between the first and the second gradient. From equation (2.4) it is clear that if there is no displacement along the gradient, the two terms will cancel. That results in no net phase shift. With diffusion, each spin acquires a random displacement and the phase shift for the individual spins will vary. Only the spins with no moment will be refocused perfectly and diffusion leads to a reduction of the signal. Regions with strongly restricted diffusion, like tumors, will therefore appear bright in the images while regions with relatively free diffusion will appear dark. This can be seen in figure 2.5a.
It can be shown that the diffusion results in an echo attenuation given by S(b, T E)SE =S0exp (−T E
T2 ) exp (−b·ADC), (2.5) wherebrefers to the diffusion-sensitizing factor, also calledb-value, andADCis the apparent diffusion coefficient. Theb-value determines the amount of diffusion weighting in the image, and it can be calculated as follows
b =γ2G2δ2(∆−δ
3). (2.6)
Ab-value equal to zero will correspond to a T2 weighted image with no diffusion weighting. Figure 2.5b shows an ADC map, and it reflects the degree of restricted diffusion. The ADC can be calculated from equation (2.5) by using at least two different b-values, and one gets
ADC =− 1
b1−b0 ln (S(b1)
S(b0)). (2.7)
(a) DWI (b) ADC map
Figure 2.5: A diffusion weighted image (a) and an ADC map (b) for a patient diagnosed with rectal cancer.